## The 7 ^{th} ICoGOIA 2018

Optimization of Green Science and Technology for Collaboration Sustainability"

Optimization is a process to achieve the ideal or optimal value of an objective function. In the discipline of mathematics, optimization alsorefers to the study of problems trying to find the minimum and maximum values of a real function. To achieve these minimum and maximum values, some processes were systematically carried out by selecting integers or real numbers that will provide optimal solutions.

The true discriminant between “easy” and “hard” optimization problems in mathematical programming is the convex/nonconvex issue. A problem is convex if it is a minimization of a convex function (or a maximization of a concave function) where the admissible points are in a convex set. The fundamental result in convex analysis says that a locally optimal solution of a convex problem is also globally optimal. This is practically very important since algorithmic termination tests occur at each iteration in the algorithm, they must be computationally very efficient; thus, virtually all termination conditions of optimization algorithms are local conditions, i.e. they test whether the current solution is locally optimal with respect to a pre-defined neighbourhood. If the problem is convex this is enough to guarantee that the solution is globally optimal. Nonconvex problems, on the other hand, may have many different local optimal, and choosing the best one is an extremely hard task.

The field of applied mathematics that studies extremal locations of nonconvex functions subject to (possibly) nonconvex constraints is called Global Optimization.Research on global optimization has been continuing rapidly and many of the findings are of new techniques thatare more sophisticated and efficient.

This year event is hosted and organised by Faculty of Mathematics and Natural Sciences Pakuan University.